Post on 07-Jan-2016
description
Attosecond light pulses for observing electron correlations in atoms
Toru MorishitaUniv. of Electro-
Communications Chofu, Tokyo
WithS. Watanabe (UEC)and C.D.Lin (KSU)
Improvements in ultra short pulse generation
Asec region
U. Keller, Nature 424, 831 (03) + private comm.
21st centuryAtto physics started in 21 century!
Attosecond in Atoms/Molecules
Rotation of molecules : pico (10-12) sec
Vibration of molecules: femto (10-15) sec
Electron motion in atoms/molecules Classical period of electron in H atom
2π* 1 au = 150 asec
Real time analysis Control/manipulate
Atomic photographyNo ordinary camera can capture the motion of electrons inside an atom. But the advent of ultrafast laser pulses brings the necessary ‘shutter speed’ for snapping them as they tumble between energy levels close to the nucleus.
L F DiMauro, Nature 419, 789 (2002)
Electron motions in atoms
Structure of multi-electron atoms
Atom , Wikipedia (Japanese)Uranium atom , Max W カーボン,原子力(それは加害者か被害者か)
Atom or molecule ? Completely different
(1s)2 (2s)2 ... Th , v, j, ...
Hartree-Fock(mean filed)
Born-Oppenheimer(adiabatic approximation)
)...ψ(r )ψ(rΨ 21 Ω)(R;Φ (R)FΨ μμ
Pauli’s exclusion principle , Shell structure
Vibration around equilibrium position Overall rotation
Energy levels of Li+(3l3l’)E
nerg
y (e
V)
1Se 1De
1Se3Po
1Po
3Do
1Do
3Pe
1De
1De
3Fe
3Fo
1Fo1Ge
1Se
3Pe
3Po
3De
1Po
3s3s
3s3p
3s3d
3p3p
3p3d
3d3d
175
176
177
178
179
1Se
3Pe
3Po
1Po
3Do
1Do
1De
3De
1De
3Fe
3Fo
1Fo1Ge
1Se
3Pe
3Po
1Po
1De
1Se
175
176
177
178
179
“Atomic” picture “Molecular” picture
T 2 1 0 21 1 0 1 0
n=0
n=1n=2
E~EN+ ω(v+1)+B[L(L+1)-T2]+GT2
n=(v-T)/2
Hund’s rule
v=N-K-1
Correlated motions, 2s2 1Se and 2p2 1Se
Atomic orbital 〔 × 〕 Molecular picture ◎〔 〕
2s2 1Se
0 θ12 π
r1r2
θ12
2p2 1Se
(θ
12)
0 θ12π
0
0
“Ground state” w.r.t. θ12
“1st excited state” w.r.t. θ12
|K=−1 〉 = 0.88|2s2s 〉 +0.46|2p2p 〉|K=1 〉 = 0.46|2s2s − 〉 0.88|2p2p 〉
How can we see the correlated electron motion ?
2s2 1Se
0 θ12π
r1r2
θ12
2p2 1Se
(θ
12)
0 θ12π
0
Oscillation period
980 asec
0 θ12π
0
|(θ
12)|
2
Coherent Sum(Wave packet)
0
Visualization of electron correlations
Vibration |Φ(α, θ12)|2
ΩE=αEβEγE
(polar plots in body-fixed frame)
ψ≈F(R) Φ(α, θ12) D(ΩE)
vibration
Breathing Rotation r1
r2
α
R
θ12
r2r1
z
Hyperspherical coordinates
Rotation|D(ΩE)|2
2 e coincidence measurement
He**
pump probe
T=0 T=Tdela
y
p1
p2
Ionization prob dipole Ionization yield
Time evolution of the momentum space wave function
“Masking” function→1 (for T→0)
1. Gaussian2. 1st order purtarbation3. Direct product of the
plane waves (Final state)
4. Velocity gauge
Double ionization
2
~
ˆ
2kj
j 2
)Tε(
tiε21
jjj21
21
2
2121
e )e,(ct),,S(
t),,S( )(ε t),,P(
pppp
pppppp
Bending vibration
Period of the vibration:960 asec
θ12
p1//ε
p2
polarization
E1=E2=2.2eV
27.2 eV,200 asec
Vibrational motion, Tomographic imaging
p1
p2
αp
Rp
θp12
p2p1
Hyperspherical coordinates in momentume space
2s2 1Se + 2p2 1Se
Ep=27.2 eV, T=200 asecE1=E2=2.2eV
Rotational motion
z’
2s2 1Se + 2p2 1De
Molecular axis
Polar plots
z’
t=0 t=1fs t=2 fs
Double ionization yield, S
Detailed structure in momentum space
Ep=27.2 eV
Ep=54.4 eV
θp12
p2p1
θp12
p2p1
p1 =p2 p1 <p2
Low energy :2electrons have the same energy
High energy :1 has most of the energy
θp12
αp
2
2
)Tε(
tiε21
jjj21
2kj
j e )e,(~ct),,S(
pppp
T=200 asec
Rotation + Vibration
Vibration and rotation can be separated
Vibration(averaged over
rotational coordinates)
Rotation(averaged over
vibrational coordinates)
Pump-probe experiments
pump (probability 10-3 - 10-4 )
He(1s2)
He **
(2s2, 2p2)
2 photons
2 color photons
1s2p
2s2p
Ti:Sa Laser + XUV
480 asec, 36.7 eV, 4x1014 W/cm2
480 asec, 38 eV,
4x1012 W/cm2
5 fsec, 1.5 eV,
4x1013 W/cm2
He ++
HHG from nsec laser
probe (probability 10-3)
480 asec, 27.2 eV, 4x1012 W/cm2
•density : 1 torr•Volume : (10μm)2 x3mm350 events/shot
Summary
Probing molecule like motions of a 2 electron atom by asec pulses
Tomographic imaging of 2-e densities in momentum space
Coherent control
Many electron systemsT
Control/Manipulate wavepacket
Similar idea to coherent control of molecules
Frank-Condon Selective
excitation using 2 pulses
etc
Adia
batic
Pote
ntia
l
He(1Se)
Ground state
Hyperradius R
2 DOubly excited states
Uμ
selective excitations
Single pulse from 1s2p Double pulse from 1s2p
2s
2s2 1Se
2p2 1Se
2p2 1De
Delay time
Ion
izati
on
pro
b
by p
um
p-p
rob
e
Ion
izati
on
pro
b.
by p
um
p
Electron energy Electron energy
Delay time
2p2 1Se
2s2 1Se
<θ
12>